y = x² − 1
Show answer
Vertex (0, −1); opens upward; x-intercepts ±1.
Free printable worksheet
Graphing Quadratics Worksheet
Nine coordinate-plane problems with completed parabola graphs in the answer key.
Algebra 1Grades 8-116 pagesAnswer key included
No email is required. Download the complete worksheet and answer key now.
Download the free PDF
What this worksheet includes
- Nine coordinate-plane problems with completed parabola graphs in the answer key.
- 6-page printable PDF with a complete answer key
- Designed for Grades 8-11 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this graphing quadratics worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 8-11 students working on algebra 1. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Algebra I worksheets.
Topic guide
How to approach graphing quadratics
A quadratic graph is a parabola. In vertex form y = a(x − h)² + k, the vertex is (h, k), the axis of symmetry is x = h, and the sign of a determines whether the graph opens up or down.
Plot the vertex first, then use symmetric x-values on both sides of the axis. The answer key includes completed parabolas so students can compare shape, direction, scale, and intercepts.
Learning objectives
- Identify a vertex and axis of symmetry
- Plot symmetric points
- Describe stretches and reflections from a
Skills to review first
- Coordinate-plane graphing
- Evaluating squared expressions
- Vertex form
Worked example
Follow the reasoning step by step
Graph y = (x − 1)² − 4.
- Identify vertex (1, −4) and axis x = 1.
- Evaluate x = 0 and x = 2 to get y = −3.
- Evaluate x = −1 and x = 3 to get y = 0.
- Plot the five points and draw an upward-opening parabola.
Solution: Vertex (1, −4); axis x = 1; points (0, −3), (2, −3), (−1, 0), and (3, 0).
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
y = −(x + 2)² + 3
Show answer
Vertex (−2, 3); opens downward; axis x = −2.
y = 2(x − 1)² − 2
Show answer
Vertex (1, −2); opens upward with a vertical stretch of 2.
Error check
Common mistakes to watch for
- Reading h with the wrong sign
- Plotting points on only one side of the axis
- Connecting points with straight segments instead of a smooth curve